{"id":225,"date":"2023-08-03T23:08:41","date_gmt":"2023-08-03T23:08:41","guid":{"rendered":"https:\/\/statorials.org\/pt\/distribuicao-continua-uniforme\/"},"modified":"2023-08-03T23:08:41","modified_gmt":"2023-08-03T23:08:41","slug":"distribuicao-continua-uniforme","status":"publish","type":"post","link":"https:\/\/statorials.org\/pt\/distribuicao-continua-uniforme\/","title":{"rendered":"Distribui\u00e7\u00e3o uniforme e cont\u00ednua"},"content":{"rendered":"<p>Este artigo explica o que \u00e9 distribui\u00e7\u00e3o uniforme cont\u00ednua e para que \u00e9 usada. Voc\u00ea tamb\u00e9m encontrar\u00e1 o gr\u00e1fico da distribui\u00e7\u00e3o uniforme cont\u00ednua e as propriedades deste tipo de distribui\u00e7\u00e3o. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%c2%bfque-es-la-distribucion-uniforme-continua\"><\/span> O que \u00e9 uma distribui\u00e7\u00e3o uniforme cont\u00ednua?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> A <strong>distribui\u00e7\u00e3o uniforme cont\u00ednua<\/strong> \u00e9 um tipo de distribui\u00e7\u00e3o de probabilidade em que todos os valores t\u00eam a mesma probabilidade de ocorrer. Em outras palavras, a distribui\u00e7\u00e3o uniforme cont\u00ednua \u00e9 uma distribui\u00e7\u00e3o em que a probabilidade \u00e9 distribu\u00edda uniformemente ao longo de um intervalo.<\/p>\n<p> A distribui\u00e7\u00e3o uniforme cont\u00ednua \u00e9 usada para descrever vari\u00e1veis cont\u00ednuas que t\u00eam probabilidade constante. Da mesma forma, a distribui\u00e7\u00e3o uniforme cont\u00ednua \u00e9 usada para definir processos aleat\u00f3rios, porque se todos os resultados tiverem a mesma probabilidade, significa que h\u00e1 aleatoriedade no resultado.<\/p>\n<p> A distribui\u00e7\u00e3o uniforme cont\u00ednua possui dois par\u00e2metros caracter\u00edsticos, <em>aeb<\/em> , que definem o intervalo <em>de<\/em> equiprobabilidade. Assim, o s\u00edmbolo para a distribui\u00e7\u00e3o uniforme cont\u00ednua \u00e9 <em>U(a,b)<\/em> , onde <em>a<\/em> e <em>b<\/em> s\u00e3o os valores caracter\u00edsticos da distribui\u00e7\u00e3o.<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-339036da3788f71282d3936dd092730c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"X\\sim U(a,b)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"92\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Por exemplo, se o resultado de um experimento aleat\u00f3rio pode assumir qualquer valor entre 5 e 9 e todos os resultados poss\u00edveis t\u00eam a mesma probabilidade de ocorrer, o experimento pode ser simulado com uma distribui\u00e7\u00e3o uniforme cont\u00ednua U(5.9).<\/p>\n<p> A distribui\u00e7\u00e3o uniforme cont\u00ednua tamb\u00e9m \u00e9 chamada de <strong>distribui\u00e7\u00e3o retangular<\/strong> . <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"formula-de-la-distribucion-uniforme-continua\"><\/span> F\u00f3rmula de distribui\u00e7\u00e3o uniforme cont\u00ednua<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> A fun\u00e7\u00e3o densidade que define a probabilidade de uma distribui\u00e7\u00e3o uniforme \u00e9 aquela dividida pela diferen\u00e7a entre <em>b<\/em> e <em>a<\/em> . Portanto, a <strong>f\u00f3rmula para a distribui\u00e7\u00e3o uniforme cont\u00ednua<\/strong> \u00e9:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-f28c4a144fb1377061b84b56968c9540_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{array}{c}X\\sim U(a,b)\\\\[2ex]f(x)=\\cfrac{1}{b-a}\\\\[4ex]x\\in [a,b]\\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"123\" width=\"99\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> Por outro lado, a fun\u00e7\u00e3o de probabilidade cumulativa da distribui\u00e7\u00e3o uniforme cont\u00ednua \u00e9 definida pela seguinte express\u00e3o:<\/p>\n<pre class=\"ql-errors\"> *** QuickLaTeX cannot compile formula:\n\\displaystyle F(x)=\\left\\{\\begin{array}{ll}0&amp;\\text{si }x&lt;h2 class=\"wp-block-heading\"&gt;&lt;span class=\"ez-toc-section\" id =\"grafica-de-la-distribucion-uniforme-continua\"&gt;&lt;\/span&gt; Graph of continuous uniform distribution&lt;span class=\"ez-toc-section-end\"&gt;&lt;\/span&gt;&lt;\/h2&gt; Since in a distribution uniform continuous probability is constant, its graphical representation is simply a function with a constant value defined in the same interval as the uniform distribution. &lt;figure class=\"wp-block-image aligncenter size-full is-resized\"&gt;&lt;img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/ 08\/distribution-uniforme-continue.png\" alt=\"Continuous uniform distribution graph\" class=\"wp-image-4498\" width=\"330\" height=\"232\" srcset=\"\" sizes=\"\"&gt;&lt;\/figure &gt; On the other hand, the cumulative probability graph of the continuous uniform distribution is as follows: &lt;figure class=\"wp-block-image aligncenter size-full is-resized\"&gt;&lt;img decoding=\"async\" loading=\"lazy \" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/distribution-uniforme-continue-probabilite-cumulative.png\" alt=\"cumulative probability plot of a continuous uniform distribution\" class= \"wp-image-4499\" width=\"247\" height=\"193\" srcset=\"\" sizes=\"\"&gt;&lt;\/figure&gt;&lt;h2 class=\"wp-block-heading\"&gt;&lt;span class=\"ez-toc -section\" id=\"caracteristicas-de-la-distribucion-uniforme-continua\"&gt;&lt;\/span&gt; Characteristics of the continuous uniform distribution&lt;span class=\"ez-toc-section-end\"&gt;&lt;\/span&gt;&lt;\/h2 &gt; The continuous uniform distribution has the following characteristics: &lt;ul&gt;&lt;li&gt; The continuous uniform distribution is defined by two real parameters, &lt;em&gt;a&lt;\/em&gt; and &lt;em&gt;b&lt;\/em&gt;, which establish the limits in which the probability is constant.&lt;\/li&gt;&lt;\/ul&gt;[latex]a,b\\in \\mathbb{R}\n\n***Error message:\nPlease use \\mathaccent for accents in math mode.\nleading text: ...continuous uniform distribution probability\nPlease use \\mathaccent for accents in math mode.\nleading text: ...if the probability is constant, its representation\nPlease use \\mathaccent for accents in math mode.\nleading text: ...a function with a constant value de\nPlease use \\mathaccent for accents in math mode.\nleading text: ...c a constant value defined in the same\nPlease use \\mathaccent for accents in math mode.\nleading text: ...On the other hand, the probability graph\nPlease use \\mathaccent for accents in math mode.\nleading text: ... part, the cumulative probability graph\nPlease use \\mathaccent for accents in math mode.\nleading text: ...nue-probabilite-cumulative.png\" alt=\"plot\n\n<\/pre>\n<ul>\n<li> A distribui\u00e7\u00e3o uniforme cont\u00ednua s\u00f3 pode assumir valores localizados no intervalo formado por <em>a<\/em> e <em>b<\/em> inclusive.<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-3d713e1ad32e4d969c10e514cd71b7d0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x\\in [a,b]\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"65\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<ul>\n<li> A m\u00e9dia de uma distribui\u00e7\u00e3o uniforme cont\u00ednua \u00e9 igual \u00e0 soma dos seus dois par\u00e2metros caracter\u00edsticos dividida por dois.<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-96d92a77b5dce5d38b2b2f3b79ac09a3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"E[X]=\\cfrac{a+b}{2}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"105\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<ul>\n<li> A vari\u00e2ncia de uma distribui\u00e7\u00e3o uniforme cont\u00ednua \u00e9 equivalente ao quadrado da diferen\u00e7a entre <em>b<\/em> e <em>a<\/em> dividido por doze.<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-1f52c10cdd7fb59fca29f8d7703e7495_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"Var(X)=\\cfrac{(b-a)^2}{12}\" title=\"Rendered by QuickLaTeX.com\" height=\"41\" width=\"149\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<ul>\n<li> A mediana de uma distribui\u00e7\u00e3o uniforme cont\u00ednua coincide com sua m\u00e9dia, portanto \u00e9 calculada pela mesma f\u00f3rmula:<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-9acd8c7117f5765f6e47060148e541e6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"Me=\\cfrac{a+b}{2}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"92\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<ul>\n<li> A distribui\u00e7\u00e3o uniforme cont\u00ednua \u00e9 sim\u00e9trica, portanto, o coeficiente de assimetria deste tipo de distribui\u00e7\u00e3o \u00e9 zero.<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-f32c2fb2ba717dc1c88c67cb82c26e9b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"A=0\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"46\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<ul>\n<li> A curtose de uma distribui\u00e7\u00e3o uniforme cont\u00ednua n\u00e3o depende de seus par\u00e2metros, \u00e9 sempre -6 dividido por 5.<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-53318cb30ff0697fd742850c405c7545_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"C=\\cfrac{-6}{5}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"71\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<ul>\n<li> A distribui\u00e7\u00e3o uniforme padr\u00e3o \u00e9 aquela distribui\u00e7\u00e3o uniforme cont\u00ednua cujos par\u00e2metros <em>a<\/em> e <em>b<\/em> s\u00e3o 0 e 1, respectivamente. <\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-be2dbf7d29ed8c8a1220e74498c77d6d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"X\\sim U(0,1)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"92\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"distribucion-uniforme-continua-y-distribucion-uniforme-discreta\"><\/span> Distribui\u00e7\u00e3o uniforme cont\u00ednua e distribui\u00e7\u00e3o uniforme discreta<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Por fim, veremos qual a diferen\u00e7a entre a distribui\u00e7\u00e3o uniforme cont\u00ednua e a distribui\u00e7\u00e3o uniforme discreta, pois s\u00e3o duas distribui\u00e7\u00f5es de probabilidade que podem ser confundidas, mas que representam conceitos totalmente diferentes.<\/p>\n<p> A principal <strong>diferen\u00e7a entre uma distribui\u00e7\u00e3o uniforme cont\u00ednua e uma distribui\u00e7\u00e3o uniforme discreta<\/strong> s\u00e3o os valores que elas podem assumir. Uma distribui\u00e7\u00e3o uniforme cont\u00ednua \u00e9 definida em um espa\u00e7o amostral cont\u00ednuo, enquanto uma distribui\u00e7\u00e3o uniforme discreta \u00e9 definida em um espa\u00e7o amostral discreto.<\/p>\n<p> Portanto, a distribui\u00e7\u00e3o uniforme discreta pode assumir apenas alguns valores em um intervalo, geralmente inteiros, enquanto uma distribui\u00e7\u00e3o uniforme cont\u00ednua pode assumir qualquer valor em um intervalo, incluindo n\u00fameros decimais. <\/p>\n<div style=\"background-color:#FFFDE7; padding-top: 10px; padding-bottom: 10px; padding-right: 20px; padding-left: 30px; border: 2.5px dashed #FFB74D; border-radius:20px;\"> <span style=\"color:#ff951b\">\u27a4<\/span> <strong>Veja:<\/strong> <a href=\"https:\/\/statorials.org\/pt\/distribuicao-uniforme-discreta\/\">Distribui\u00e7\u00e3o uniforme discreta<\/a><\/div>\n","protected":false},"excerpt":{"rendered":"<p>Este artigo explica o que \u00e9 distribui\u00e7\u00e3o uniforme cont\u00ednua e para que \u00e9 usada. Voc\u00ea tamb\u00e9m encontrar\u00e1 o gr\u00e1fico da distribui\u00e7\u00e3o uniforme cont\u00ednua e as propriedades deste tipo de distribui\u00e7\u00e3o. O que \u00e9 uma distribui\u00e7\u00e3o uniforme cont\u00ednua? A distribui\u00e7\u00e3o uniforme cont\u00ednua \u00e9 um tipo de distribui\u00e7\u00e3o de probabilidade em que todos os valores t\u00eam a [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[12],"tags":[],"class_list":["post-225","post","type-post","status-publish","format-standard","hentry","category-probabilidade"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v21.5 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>\u25b7Distribui\u00e7\u00e3o uniforme cont\u00ednua<\/title>\n<meta name=\"description\" content=\"Aqui voc\u00ea encontrar\u00e1 o que \u00e9 distribui\u00e7\u00e3o uniforme cont\u00ednua, sua f\u00f3rmula, gr\u00e1fico e caracter\u00edsticas da distribui\u00e7\u00e3o uniforme cont\u00ednua.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/statorials.org\/pt\/distribuicao-continua-uniforme\/\" \/>\n<meta property=\"og:locale\" content=\"pt_PT\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"\u25b7Distribui\u00e7\u00e3o uniforme cont\u00ednua\" \/>\n<meta property=\"og:description\" content=\"Aqui voc\u00ea encontrar\u00e1 o que \u00e9 distribui\u00e7\u00e3o uniforme cont\u00ednua, sua f\u00f3rmula, gr\u00e1fico e caracter\u00edsticas da distribui\u00e7\u00e3o uniforme cont\u00ednua.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/statorials.org\/pt\/distribuicao-continua-uniforme\/\" \/>\n<meta property=\"og:site_name\" content=\"Statorials\" \/>\n<meta property=\"article:published_time\" content=\"2023-08-03T23:08:41+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-339036da3788f71282d3936dd092730c_l3.png\" \/>\n<meta name=\"author\" content=\"Dr. benjamim anderson\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Escrito por\" \/>\n\t<meta name=\"twitter:data1\" content=\"Dr. benjamim anderson\" \/>\n\t<meta name=\"twitter:label2\" content=\"Tempo estimado de leitura\" \/>\n\t<meta name=\"twitter:data2\" content=\"5 minutos\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"WebPage\",\"@id\":\"https:\/\/statorials.org\/pt\/distribuicao-continua-uniforme\/\",\"url\":\"https:\/\/statorials.org\/pt\/distribuicao-continua-uniforme\/\",\"name\":\"\u25b7Distribui\u00e7\u00e3o uniforme cont\u00ednua\",\"isPartOf\":{\"@id\":\"https:\/\/statorials.org\/pt\/#website\"},\"datePublished\":\"2023-08-03T23:08:41+00:00\",\"dateModified\":\"2023-08-03T23:08:41+00:00\",\"author\":{\"@id\":\"https:\/\/statorials.org\/pt\/#\/schema\/person\/e08f98e8db95e0aa9c310e1b27c9c666\"},\"description\":\"Aqui voc\u00ea encontrar\u00e1 o que \u00e9 distribui\u00e7\u00e3o uniforme cont\u00ednua, sua f\u00f3rmula, gr\u00e1fico e caracter\u00edsticas da distribui\u00e7\u00e3o uniforme cont\u00ednua.\",\"breadcrumb\":{\"@id\":\"https:\/\/statorials.org\/pt\/distribuicao-continua-uniforme\/#breadcrumb\"},\"inLanguage\":\"pt-PT\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/statorials.org\/pt\/distribuicao-continua-uniforme\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/statorials.org\/pt\/distribuicao-continua-uniforme\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Lar\",\"item\":\"https:\/\/statorials.org\/pt\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Distribui\u00e7\u00e3o uniforme e cont\u00ednua\"}]},{\"@type\":\"WebSite\",\"@id\":\"https:\/\/statorials.org\/pt\/#website\",\"url\":\"https:\/\/statorials.org\/pt\/\",\"name\":\"Statorials\",\"description\":\"O seu guia para a literacia estat\u00edstica!\",\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\/\/statorials.org\/pt\/?s={search_term_string}\"},\"query-input\":\"required name=search_term_string\"}],\"inLanguage\":\"pt-PT\"},{\"@type\":\"Person\",\"@id\":\"https:\/\/statorials.org\/pt\/#\/schema\/person\/e08f98e8db95e0aa9c310e1b27c9c666\",\"name\":\"Dr. benjamim anderson\",\"image\":{\"@type\":\"ImageObject\",\"inLanguage\":\"pt-PT\",\"@id\":\"https:\/\/statorials.org\/pt\/#\/schema\/person\/image\/\",\"url\":\"https:\/\/statorials.org\/pt\/wp-content\/uploads\/2023\/10\/Dr.-Benjamin-Anderson-96x96.jpg\",\"contentUrl\":\"https:\/\/statorials.org\/pt\/wp-content\/uploads\/2023\/10\/Dr.-Benjamin-Anderson-96x96.jpg\",\"caption\":\"Dr. benjamim anderson\"},\"description\":\"Ol\u00e1, sou Benjamin, um professor aposentado de estat\u00edstica que se tornou professor dedicado na Statorials. 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